Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit

TL;DR

This paper derives generalized three-particle Bargmann-Wigner equations from a nonlinear isospinor-spinor field, finds mixed symmetry solutions in the strong-coupling limit, and interprets three solution manifolds as three generations of leptons and quarks.

Contribution

It introduces a new class of mixed symmetry solutions to three-particle equations and links these solutions to the three generations of fundamental fermions.

Findings

Derived generalized three-particle Bargmann-Wigner equations.

Calculated spin 1/2 bound-states with mixed symmetries.

Interpreted three solution manifolds as three generations of leptons and quarks.

Abstract

Starting from a nonlinear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, a special class of spin 1/2 bound-states are calculated. These solutions which are antisymmetric with respect to all indices, have mixed symmetries in isospin-superspin space and in spin orbit space. As a consequence of this mixed symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these solution manifolds are interpreted as the three generations of leptons and quarks. This interpretation will be justified in a forthcoming paper.